1. Field of the Invention
The invention relates to a method and network configuration for obtaining the gradient of the output signals of a given network for processing discrete-time signals relating to network parameters, wherein the network includes a first subnetwork having only delay-free elements, being acted upon by input signals and emitting the output signals, and a second subnetwork having only time-lag elements to which signals from the first subnetwork are supplied and which feeds the signals back to the first subnetwork with a delay.
2. Description of the Related Art.
Adaptive networks, such as adaptive digital filters, are of major significance in many areas of discrete-time signal processing, particularly in the fields of systems analysis, echo compensation in two-wire/four-wire transitions, line distortion correction and speech processing. The characteristic of such adaptive networks, in comparison with constant networks, is that the network parameters that determine the transfer properties are optimally adjusted with respect to a Q function. A Q function of that kind is, for instance, obtained by minimizing the mean quadratic error of the output signal at the adaptive network with respect to a reference signal. For instance, in Optimization Theory with Applications, published by John Wiley and Sons, New York, 1969, D. A. Pierre discloses a method in which the partial derivations (gradient) of the Q function are formed in accordance with the network parameters to be adapted. However, for most quality criteria, that method is traceable to the formation of the partial derivations of the output signal of the adaptive network in accordance with the network parameters.
In non-recursive structures such as finite impulse response filters and transversal filters, the output signal is a linear combination of variously delayed and weighted input signals, and as a result the gradient formation is still relatively easy to perform.
In contrast, in recursive structures, such problems are substantially more complex and have thus far been solved only for very specialized structures, such as is described by S. Horvath in Adaptive rekursive Entzerrer fur schnelle Datenubertragung [Adaptive Recursive Distortion Correctors for Fast Data Transfer], ETH Zurich [Engineering College of Zurich], dissertation ETH 5860, 1977, for the cascade circuit of quadratic systems, for first and second canonic structures and for lattice filters, as well as for filters of Gray and Markel structure, as is disclosed, for instance, by D. Parikh, N. Ahmed and S. D. Stearns in IEEE Trans. On Acoustic Speech and Signal Proc., Vol. ASSP-28, No. 1, February 1980. The disadvantages of the known methods are that they are relatively expensive and each is valid only for a specific, very specialized structure.
It is accordingly an object of the invention to provide a method and network configuration for obtaining the gradient of the output signals of a given arbitrary network for processing discrete-time signals relating to the network parameters, which overcomes the hereinafore-mentioned disadvantages of the heretofore-known methods and devices of this general type.